Modeling Quantum Noise in Nanolasers Via Markov Chains Accurately Predicts Fluctuations in Laser Output

Fluctuations in a laser’s output, stemming from the inherent randomness of light emission, present a significant challenge for modelling laser behaviour, particularly in the increasingly important field of nanophotonics. Matias Bundgaard-Nielsen, Gian Luca Lippi, and Jesper Mørk, from the Technical University of Denmark and Université Côte d’Azur, now demonstrate a powerful new approach to accurately modelling quantum noise in lasers of all sizes. Their work reveals that by treating the number of electrons within the laser as discrete values and framing the process as a Markov chain, they achieve quantitative accuracy across a broad range of laser types, from nanoscale devices to macroscopic systems. This method surpasses traditional approaches, which struggle below the laser threshold, and offers a robust framework for understanding and optimising laser performance in diverse applications.

Markov Chains Model Nanolaser Quantum Noise

Understanding random fluctuations in laser emission, particularly from nanolasers, is crucial for optimizing their performance in various applications. This work investigates the quantum noise characteristics of nanolasers by employing a Markov chain approach, allowing for detailed analysis of the statistical properties of the emitted light. The method models laser dynamics as a process where transitions between quantum states represent the emission and absorption of photons, enabling the calculation of key noise parameters that quantify deviations from predictable behaviour. Results demonstrate the ability to accurately predict the noise behaviour of nanolasers under various operating conditions, including different pump powers and energy losses within the laser cavity.

The study reveals that quantum confinement effects and enhanced light-matter interactions play a crucial role in shaping the noise spectrum, leading to both suppression and enhancement of quantum noise depending on specific device parameters. This detailed understanding is essential for optimizing nanolaser performance in applications such as quantum communication, sensing, and spectroscopy. Conventional approaches often incorporate fluctuations into laser models using random forces, but this proves inadequate for nanolasers. This work demonstrates that laser quantum noise can be quantitatively computed for a broad class of lasers by starting with simple rate equations and assuming that both the number of photons and excited electrons take only discrete values. The success of this model stems from its foundation as a Markov chain, derived from the fundamental equations governing the system’s behaviour, and its simplification to established theoretical frameworks with many photons.

Quantum Noise and Modelling Limits

This research establishes a formal connection between complex equations and a laser model that treats laser populations as discrete integer variables. By demonstrating that this discrete model simplifies to rate equations in the limit of many photons, the team clarifies the valid regimes for different approaches to modelling quantum noise in nanolasers. A comprehensive numerical comparison of accuracy and computational efficiency reveals distinct strengths for each method investigated, with the Gillespie method proving most efficient for small populations and tau-leaping excelling with intermediate system sizes. Numerical solutions to rate equations, however, are accurate and efficient only for very large populations where quantum effects are minimal. The team identified a limitation of numerically solving rate equations, noting that the approach can produce inaccurate results below the lasing threshold due to the potential for unphysical negative populations. The researchers highlight the versatility of their discrete model, which remains numerically stable and can be extended to explore more complex laser systems, such as those incorporating non-linear mirrors or investigating nanolaser modulation, identifying these areas as promising avenues for future research.

Quantum Noise and Modelling Methods

Accurately modelling quantum noise in lasers and optical amplifiers is paramount, necessitating stochastic methods due to the inherent randomness of quantum mechanics. Computational efficiency is crucial, leading to the use of approximate methods and specialized solvers. The availability of open-source software and a multidisciplinary approach spanning physics, mathematics, computer science, and engineering further characterize the field. Researchers utilize stochastic simulation methods, including the Gillespie algorithm, an exact method for simulating chemical kinetics, and tau-leaping, an approximate method that speeds up simulations.

Langevin dynamics, a classical molecular dynamics method that includes random forces to simulate thermal fluctuations, is also employed, alongside master equation solvers and Markov chains, a mathematical system that undergoes transitions between states. Researchers also utilize programming languages like Python and Julia for implementing and analysing simulations, highlighting the importance of numerical methods and software, including differential equation solvers and specialized solvers for quantum master equations. This work represents a comprehensive overview of the theoretical and computational tools used to study quantum noise, open quantum systems, and the dynamics of light-matter interactions.